Sunday, April 17, 2011

When Jews were crossing the sea, two events happened. One: the Heavens descended down to the Earth. Two: the Earth was elevated up to the Heavens.

Alter Rebbe explains in a ma'amor that sea represents G-d's Speech, which is the sphera of Malchus of Atzilus. All three concepts — sea, speech and Malchus — have in common that they exist both to unite and to separate. (Interestingly, this is also the idea seen in the mitzva of Havdala.)

In order to express his thoughts to others, a person must speak. But at the same time, speech separates the one who receives the person's ideas from the person's mind. Once spoken, thoughts do not exist anymore in the same state as they did in the mind. They are made accessible, crystallized — and also limited.

Similarly, the sphera of Malchus of Atzilus exists to create the lower worlds, to direct to them the light of its own world — but at the same time, Malchus separates the three created worlds from Atzilus.

In this way, it is also similar to the sea. Malchus is called "the great sea", because, just like "all rivers fall into the sea", the six emotional spheros (Ze'er Anpin) collect their lights into Malchus. And just like the sea separates the marine creatures from the earth creatures, since the former cannot breath above the water and the latter cannot breath below it, Malchus of Atzilus makes sure that the phenomena of Atzilus cannot exist in the created worlds (they would "suffocate" from such limited Light) and that, conversely, the created beings cannot ascend into Atzilus (since they can only receive the Light in a limited form through the vessels of their worlds and would "dissolve" in Atzilus).

This, then, was what happened during the Kriyas Yam Suf, the splitting of the Sea of Reeds: the Great Sea, Malchus of Atzilus, split. Two views (that of the Zohar and that of Arizal) exist regarding what happened:

The limitation of Malchus of Atzilus was stopped so that the Lights of Atzilus could descend and unite with the physical universe below and Jews inhabiting it.

When Malchus "split", the Jews were elevated into Atzilus.

One of the views places emphasis on the fact that the Jews were able to continue walking on dry land towards their destination. If there was a sea on their way — then the sea split, but that's not the main point. The other view's emphasis is on the fact that Jews were plunged into the middle of the sea. The dry-land aspect of the journey was only a means for the Jews to survive their journey into the realm normally uninhabitable.

Alter Rebbe explains in his ma'amor that both these points of view are correct: the Heavens split and the Supernal Lights were able to reach the physical Universe and the Jews, and, at the same time, Jews themselves were elevated to the level of the Supernal Lights.

Kriyas Yam Suf was an event that prepared the Jews for the receiving of Torah. The two spiritual aspects of the Splitting corresponded to two aspects of Mattan Torah: the fact that it was received (by Jews) and the fact that it was given (by G-d). On the one hand, Jews are never lofty enough to receive the Wisdom and Will of HaKodosh Boruchu Himself. On the other, G-d is too lofty and elevated above the physical aspects of the world for His Will to be associated with them. Both these limitations (so to speak) were broken at the Kriyas Yam Suf.

This explains what Torah and mitzvos accomplish. On the one hand, they elevate the person who performs them to the state of holiness ("asher kideshanu bemitzvoisav..."). On the other, they introduce G-dliness into the physical aspects of the world and the levels of our souls associated with them, creating a dwelling in the lower worlds for G-d.

On the more abstract level, the two aspects correspond to yichuda ila'ah and yichuda tata'ah: the Upper Unity and the Lower Unity. The first is the concept that ein od milvado — there is nothing but G-d, in a simple, literal sense. Even though on our level of reality, the worlds exist, in relationship to G-d's Essence, nothing exists. (Imagine this as the function of y = 1/x taken to infinity. The larger the x, the smaller the y — but still always finite. But when x = ∞, then y = 0, mamosh.) And obviously, our point of view is "wrong" when compared with G-d's point of view. On the ultimate level of truth, nothing but G-d exists.

The concept of Lower Unity corresponds to the idea of G-d's unity with all of creation. From this point of view, all of the worlds exist, but they are still completely one with G-d, in a perfect (albeit complex) unity. This is revealed by the fact that He creates them all every single moment (or, to put it more correctly, He creates their every moment). That His thought pervades them all. That for Him, they exist as one point, with all dimensions compressed into a single idea.

For our avoida, this means that two levels of bittul exist. These two levels are represented by two colors of flame (and two colors of tzitzis strings): white and blue. Flame is a symbol of bittul: the desire of the soul to "rise" and nullify itself to G-d. There is the "blue" level, the part of the flame that hugs the wick. Then there is the white level, the part of the flame which never even touches the wick.

In our lives, the blue flame corresponds to the idea of realizing and revealing G-d's omnipresence in our lives (on the one hand, the flame rises from the candle; on the other, it is still connected to the wick). The fact that everything that happens in our lives is connected to G-d and is only due to G-d's Will and Kindness. And, respectively, that everything that we do in our lives must be connected to G-d. We cannot do anything "stam". Everything must be, one way or another, an aspect of avoidas Hashem.

And then there is the level where nothing but G-d exists. This level is achieved in our avoida through contemplation about G-d, as we learn about Him in Chassidus, during davening, on Shabbos and holidays. On this level, not only is G-d one with the world, but G-d is One — the only one.

As Alter Rebbe's ma'amor teaches, both aspects are extremely important and both aspects are the part of our journey to Har Sinai — to the point in the world's history, where G-d's Essence will be revealed. And this time, not for a short time only, as it happened during Mattan Torah, but forever. May it happen speedily in our days.

Wednesday, April 13, 2011

So, some people say that [...] an electron is actually a four-dimensional wave. Its interaction with quantum labeler changes its energy such that it becomes collapsed. Its interaction with quantum eraser restores the same energy level and restores the electron's wave — but, it restores it back in four dimensions (including the time), such that the electron is now a wave "again", not just in the space, but also in the time, including the point in the past where it passed through the slit.

(I think this would be a good moshol for teshuva that [one] could use. When a person does teshuva, he goes back and erases his sin — in fact, turns his sin into a mitzva. This is because, although to our perception, we exist as a point on the time line, always moving forward, in reality, we exists in all possible dimensions at the same time. And, by making teshuva, we interact, with G-d's help, with ourselves in the past.)

I wrote "with G-d's help" deliberately, and not just because it is customary to do so when you're saying that you will accomplish something (i.e., as a more frum way of saying "hopefully"). There was some thought at the back of my mind when I was writing the above, but I didn't attend to it fully at the time. This morning, I thought more about it.

In reality, perhaps the moshol is not the most accurate. Because even though according to the above model, the electron is a four-dimensional wave (and there are other models that don't require that), there is no indication that we exist as a four-dimensional being, and that our past is as much an aspect of our reality as the present. I.e., there is no indication that we, "ourselves", can interact with our past, just like we can interact with our space by picking up a cup¹.

On the other hand, for G-d Almighty, past, present and future exist as one reality on the same level. The space, time, and whatever other physical or spiritual dimensions — all exist as one point, one singularity, for G-d.

(As an aside, I wanted to mention that my professor of German would sometimes show us German movies — for 15 minutes at the end of every class. After he was done with a particular DVD, he would "rewind" it, like one would a tape. And by that I mean he would press << on his DVD remote and wait until the movie reached the beginning. Eventually, someone explained to him that you don't have to rewind DVDs, just like you don't have to "rewind" books. Although, of course, a movie or a novel do no exist on a DVD or in a book as one single nekuda...)

That is why, if we reach to the Essence of G-d, to the point above all structure, space and time, we are able to change the past, so to speak, since past and present there are one. We do this by reaching to our yechida sh'b'nefesh, the essence of our soul, by performing teshuva, repentance. This is really the point of Yom Kippur — why it is so holy. Not that it is the day on which the sins are forgiven, but that it is the day on which we are one with Hashem, and on that level, a) no separations (sins) can exist between us and Him, and b) we are able to nullify our sins or even change them into mitzvos.

That is why the concept of teshuva is so important in Chassidus. If you will, teshuva is the reason why the world was created. The world exists as a seemingly separate entity from G-d. Our job is to reveal G-d's Essence in the world, to reveal oneness of G-d with the world. So, this is the ultimate teshuva — teshuva for the whole world. Space and time, perhaps. Because by revealing that the world is one with G-d today, we go back in the time and transform the "sin" (so to speak) — the existence of the world for all millenia in a state of concealment of G-d — into a "mitzva", revelation of G-d. We show that all the existence of the world, even in a form of concealment, was only for the purpose of (eventual) revelation of G-d in the world.

This way, we achieve perfect oneness of G-d with the world — not just with the space of the world, but also with the time of the world. May it happen speedily in our days.

___________
¹ Of course, nothing we do even in our everyday reality is "by ourselves". Everything we do is with the help of G-d, since G-d is creating the Universe every second. So, if I want to move a cup, I have to will it, and then G-d responds to that with the Universe re-created with cup moved (plus everything that needs to happen in my brain, muscles, etc., for me to move my hand).

Which means that on the one hand, when we punch someone's nose, we are asking Hashem to do something not nice. On the other hand, when someone punched us in the nose, it was really Eibeshter that did so — the other guy's decision to do so is between him and Eibeshter. Our nose would not get punched had we not deserved it.

Tuesday, April 12, 2011

Today is the 50th anniversary of the flight of the first man to space, Yuri Gagarin, sent there by the Soviet Union. He boldly flew... etc., etc.

To commemorate this, a few jokes:

Russians sent the first man to space. They also sent the first satellite to space, the first dog and the first hot-dog (when the first dog was on the way down).

Russians send the first man to space. A Ukrainian shepherd calls out to another Ukrainian shepherd:
— Mikola!
— What?
— Russians flew to space!
— All of them?
— No, just one.
— So, why are you bothering me?

Americans spent millions of dollars and decades of research on developing a pen that would work in zero gravity. Russians use pencils.

All jokes aside, when Gagarin came back, he said: "The Earth is very beautiful. Treasure it."

Monday, April 11, 2011

To clarify what I said in one of the previous posts about consciousness and quantum mechanics. (This is from a very limited and probably very erroneous understanding of this topic. Alternatively, you can just skip the mumbo-jumbo below and just watch this — no discussion of four-dimensional waves can happen without a reference to this scene.)

From what I understand, the idea is that measurement affects what "decision" the electron makes. According to some people, measurement is congruent with human consciousness. In reality, that's not necessarily the case, because just measurement alone (i.e., interaction with a non-conscious measuring device), without the consciousness, is enough to collapse the wave.

The same goes for Schrödinger's Cat. According to the "paradox", until you open the box with the cat, the cat exists as both alive and dead, and then your measurement (and, some people would say, consciousness) influences the reality.

(By the way, Schrödinger himself never postulated this as the state of events — he used his Cat as an argument ad absurdum to show that our understanding and mathematical apparatus of quantum mechanics are incomplete. But, interestingly enough, around the same time, Einstein, Podolsky and Rosen published a paper, in which they showed that, following mathematics of quantum mechanics, you can have a state of events when particles are separated spatially and yet are instantaneously linked to each other. I.e., just because they are far apart from each other doesn't mean they are distinct, independent entities. This was also an ad absurdum paper, but this phenomenon was shown to be true — it is now known as quantum entanglement. So, not all ad absurdums are absurd.)

Anyway, the point is that it doesn't require consciousness to collapse a function. What actually is required is measurement, but why that is the case is unclear. Some people say it's the interaction with the "macro-world" which collapses the function (in which case, Schrödinger's cat is exclusively dead or exclusively alive as soon as the electron interacts with the poisonous gas machine). But, recently they've done another experiment, in which they "labeled" the electron itself as having passed through either right or left slit (this way, one would know, once the electron reaches the screen, which slit it had passed through). Well, if you do that, you, as expected, collapse the interference pattern.

But then, if you put a "quantum eraser" between the slits and the screen, which will erase the "label" from the electron, you actually restore the interference pattern. So, when the electron interacts with the macro-world once, this collapses the wave function. But, if it interacts with the world twice, this restores the wave function! So, in the end, what's important is whether the electron's passage through one or the other slit is measured. If it is measured, the wave collapses. If the measurement information is erased, the wave is restored.

Again, this doesn't necc. say anything about the importance of consciousness. I think that we just have no idea what really happens when the electron wave collapses.

The unique thing about the Quantum Eraser experiment is that once electron wave collapses at the slit, there is no way that interaction of the electron's wave with itself can happen — but then, if you put up the quantum eraser, it restores the interference pattern... meaning, it is as if it told the electron: "Now go back to the past and actually interfere with yourself".

So, some people say that this shows that an electron is actually a four-dimensional wave. Its interaction with quantum labeler changes its energy such that it becomes collapsed. Its interaction with quantum eraser restores the same energy level and restores the electron's wave -- but, it restores it back in four dimensions (including the time), such that the electron is now a wave "again", not just in the space, but also in the time, including the point in the past where it passed through the slit. (I think this would be a good moshol for teshuva that Tzvi Freeman et al. could use. When a person makes a teshuva, he goes back and erases his sin — in fact, turns his sin into a mitzva. This is because, although to our perception, we exist as a point on the time line, always moving forward, in reality, we exists in all possible dimensions at the same time. And, by making teshuva, we interact, with G-d's help, with ourselves in the past.)

But, another interpretation of the Quantum Eraser experiment could be that when a wave function collapses, it does not collapse "completely", so to speak. It just passes from the state where it influences reality to the state where it does not, but it (and its interaction with itself) always exists in potential, alongside with the electron's "collapsed" path.

So, imagine that when electron passes through the two slits, all the possible paths it can take exist simultaneously — and interfere with each other in a wave-like fashion. Then, when the electron is "labeled", its wave function collapses, and only one of the paths exists "in reality". The other paths, however, do not disappear. They are still out there, hanging like punctured lines, "in potential".

If the electron is allowed to reach the screen, the potential paths and their potential interactions are never allowed to influence the reality of the electron's trajectory.

If, however, the electron interacts with the quantum eraser, the latter reverses whatever effect the quantum labeler did (by restoring the energy levels to the former, etc.). This restores the electron's state as a wave and all the "potential" possible paths become real (all at once) again — as well as their, so far only potential, interactions.

In this interpretation, there is no need to do something as esoteric as imagining the electron as a four-dimensional wave interacting with itself not only in space, but also in time. Although, perhaps the concept of potential paths existing in a state of semi-reality is even more esoteric.

Update: Regarding probabilities, a conversation in the kitchen:
— Did you know that on average, a human foot sweats a cup a day?
— Not my foot.
— I said “on average”.
— Just sayin’. My feet don’t sweat no cups per day.

Wednesday, April 6, 2011

Looking at the graph above made me think about how in "historic" sciences, such as Evolutionary Biology or Geology, we extrapolate the existing state of the world backwards in time to try to paint a picture of the past. This is like standing on the right part of the "blue" graph above (the "real" graph) and looking backwards, to x < 0.

But what if the world did not exist in the same state of "reality"? For example, it existed not in a material form, like today, but in some sort of spiritual form. And today, when we look at the world, we find the remnants of those "spiritual" processes (as they "materialized" themselves once the world passed x = 0) and, trying to interpret them, create a distorted picture of the past (since we have access only to the "real" part of the "function").

For instance, Evolutionary Biology shows relationship between species. Extrapolating back billions of years, it interprets it as descent with modification due to natural selection. And, considering that today descent with modification due to both natural and human selection is observed, that there is no reason to believe that it did not happen in the past, and that there is evidence consistent with the descent with modifications due to natural selection, all this seems to present strong evidence in favor of Theory of Evolution. (Even though many mechanisms are not clear, and many aspects of the evidence remain unexplained. So, nu, in every set of ideas you have holes and gaps. From physics to, lehavdil, Gemara. Just because there is a discontinuity in the function doesn't mean that we can't work with the function.)

But what if descent with modification did happen (and there may even have been selection), but not in "nature", since the nature, with the rest of the physical world, did not exist? Perhaps what really happened was some sort of evolutionary "spiritual" process that happened before the creation of the world and, during the first week 6771 years ago, "created" the species (which would not contradict G-d creating the species, since "He and His life-giving emanations are one; He and His garments are one" — i.e., G-d envelops Himself and becomes one with the spiritual tools with which He creates the worlds and all that is in them).

And now we see merely the material "shadow" of those spiritual events.

(Yes, I know I am misusing the concept of imaginary and real numbers. This is just a graphic illustration. There need not be a strict coherence between the moshol and the nimshal. Also, you can interpret "imaginary" as a product of our extrapolation, or you can say that "imaginary" = spiritual, while "real" = material.)

Tuesday, April 5, 2011

In his book, Wheels, Life and Other Mathematical Amusements,Martin Gardner asks:

Single-panel gag cartoons, like Irish bulls, are often based on outrageous logical or physical impossibilities. Lewis Carroll liked to tell about a man who had such big feet that he had to put his pants on over his head. Almost the same kind of impossibility is the basis of a famous New Yorker cartoon by Charles Addams of a woman skier going down a slope. Behind her you see her parallel ski tracks approaching a tree, going around the tree with a track on each side and then becoming parallel again.

Suppose you came on a pair of such ski tracks on a snowy slope, going around a tree exactly as in Addams's cartoon. Assume that they are, in truth, tracks made by skis. Can you think of at least six explanations that are physically possible?

In his Answers section, after listing the possibilities, he jokingly brings a cartoon by J. Hart. I call this situation a wave function build-up:

Everyone knows about wave function collapse. (If you don't want to read about it, skip to the quote from Martin Gardner.)

In short, imagine you wanted to determine where I am right now. Without knowing my exact location, but knowing where I might be, you can assign probabilities to a number of locations. I can be at my home. I can be at work. I can be on my way in between. I can be in a grocery store. I can be shopping for a new pair of headphones at BestBuy. And so on. I can also be in Maryland — but with much lower probability than in the above places, although probability greater than zero. Probability of me being on the moon right now is very-very close to zero. Probability of me being in Alpha Centaura solar system is zero.

So, you can draw a "probability cloud", with each location's density proportional to the probability of my being there.

At different times, my probability cloud changes shape. For instance, on Shabbos, it becomes restricted to the walking distance around my house, and it's densest at my house, my shull, and the homes of the few people that I go to lunch to on Shabbos with my wife. Around Peisach time, my probability wave will shift to Skokie, when I will be visiting my in-laws. And so on.

The interpretation of the probability cloud regarding me is that I may be found in any of the locations on the cloud. In reality, however, at any given moment of time, I am at only one of those locations. It's not like 50% of me is at my work, 40% is at home, and 10% on the highway in between. The probability cloud is a result of your lack of precise knowledge about my location. If you put a GPS device on me, my probability cloud in your measurement will shrink to whatever the limitations of the device's accuracy are (e.g., plus-minus ten meters).

Well, in the quantum world, it's different. An electron's probability cloud has reality. The electron really exists at the same time in all the places represented by its probability cloud — the greater the probability, the more it exists there. It's as if the electron's metzius was smeared over the space.

(different shapes of electron's orbitals)

Well, if you make an experiment of shooting an electron (or any other quantum "particle") through two slots many times, as everyone knows, the collection of the marks on the screen where the electron hits will have interference pattern — a pattern similar to what you would see if you sent two waves of any kind through two slots (e.g., waves of water or a wave of light).

As waves go through space, they interfere with each other, partially cancelling each other in some places and super-imposing on each other in others, forming this pattern in the end:

In contrast, if you shoot a bunch of pellets through two slots, those pellets that pass through will form two parallel bars of marks on the screen — since the pellets don't interfere with each other (as waves do) when they fly.

Now, if you shoot a bunch of electrons at the screen, they will form wave-like interference patterns seen above. This suggests that electrons interfere with each other as waves when they fly through space. But, even more shockingly, if you shoot electrons one at a time, the interference pattern will be the same (with each bright bar representing places of greater probability for the electrons to hit the screen). It's as if the electron is interfering with itself when flying through space — which means that it doesn't fly as a particle, but as a probability wave, a wave of metzius, if you will, which interferes with itself just like a water wave passing through two slits.

In the last part of the experiment, if you put a detector next to one of the slits, to see if the electron "really" passes through the slit, the interference pattern forming on the screen will be only two bars. It's as if when you observe the electron, you force it to pick a slit. While flying unobserved, the electron is free to be as "scatter-brained" and indecisive as it wants (or as its wave function dictates). But, when meeting a detector (and, whatever Tzvi Freeman tells you, it's not the human consciousness that the electron meets, but simply a piece of macro-world, a detector, which will work even if the human being with his consciousness went to lunch), the electron has to make a decision, and it will decide for sure that it wants to fly through the one slot only or through the other.